。
She made the children clean their own rooms.
Literal
She [topic-は] children [target-に] own self [genitive-の] room [object-を] cleanly clean-up made.
A multi-layered causative sentence. 掃除させる is the causative of 掃除する ('to clean'). The agent of the caused action takes に — 子供たちに ('made the children'). The object of cleaning takes を — 部屋を. 自分自身 ('one's own self') is an emphatic reflexive, doubled from the simpler 自分 for extra force ('their *very own* rooms'). きれいに is the adverbial of きれい ('clean, pretty') — 'cleanly, into a clean state.'